A projectile is fired vertically up from the bottom of a crater (big hole) on the moon The depth of the crater is `R//100` where `R` is the radius of the moon if the initial velocity of the projectile is the same as the escape velocity from the moon surface The maximum aproximate height attained by the projectile above the lunar (moon) surface is `xR` Find the greatest integer of `x` .

Answer

99.5 R

Explanation

Total energy at A=Total energy at B
`(KE)_(A)+(PE)_(A)=(PE)_(B)`
`(1)/(2)mxx(2GM)/(R)+[(-GMm)/(2R^(3)){3R^(2)-((99R)/(100))^(2)}]=-(GMm)/(R+h)`